Simplify the following expression: $ z = \dfrac{9k}{4k + 4} - \dfrac{3}{10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{9k}{4k + 4} \times \dfrac{10}{10} = \dfrac{90k}{40k + 40} $ Multiply the second expression by $\dfrac{4k + 4}{4k + 4}$ $ \dfrac{3}{10} \times \dfrac{4k + 4}{4k + 4} = \dfrac{12k + 12}{40k + 40} $ Therefore $ z = \dfrac{90k}{40k + 40} - \dfrac{12k + 12}{40k + 40} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{90k - (12k + 12) }{40k + 40} $ Distribute the negative sign: $z = \dfrac{90k - 12k - 12}{40k + 40}$ $z = \dfrac{78k - 12}{40k + 40}$ Simplify the expression by dividing the numerator and denominator by 2: $z = \dfrac{39k - 6}{20k + 20}$